A gas effuses into a vacuum through a small hole of area A. The particles are th

Question

A gas effuses into a vacuum through a small hole of area A. The particles are then collimated by passing through a very small circular hole of radius a, in a screen a distance d from the first hole. Show that the rate at which particles emerge from the second hole is , where n is the particle density and (v) is the average speed. (Assume that no collisions take place after the gas effuses through the second hole, and that .) Show that if a gas were allowed to leak through a small hole into an evacuated sphere and the particles condensed where they first hit the surface they would form a uniform coating.

Explanation / Answer

A gas effuses into a vacuum through a small hole of area A. The particles are then collimated by passing through a very small circular hole of radius a, in a screen a distance d from the first hole. Show that the rate at which particles emerge from the second hole is 1 4 n A v a 2 d 2 14nAva2d2 , where n is the particle density. We also assume that no collisions occur after the gas effuses through the first hole.

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